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将Lyness高维超立方体对称求积公式制订规则应用于四维、六维情形,得出了具有9次和11次精度四维超立方体对称求积公式W5(4)和W6(4),以及具有9次和11次精度六维超立方体对称求积公式W5(6)*和W6(6)*。相对于同等精度高斯求积公式,它们具有更少的函数求值次数,求值次数最低可低至185和505次,以及465和1825次。将导出的四维、六维求积公式分别应用于任意导体面目标RWG基伽略金矩量法阻抗元素计算以及非均匀介质目标扩展RWG伽略金矩量法阻抗元素的计算中,计算结果表明在剖分单元电尺寸不超过λ/4的常规应用下,两组四维空间求积公式相对精度在1e-6量级,两组六维空间求积公式求积精度在1e-4量级,求积效果理想。
The formulas of symmetric quadrature formula of Lyness hypercube are applied to four-dimensional and six-dimensional cases, and the formulas of four-dimensional and four-dimensional hypercubes symmetric quadrature W5 (4) and W6 (4) Eleven Accuracy Six-Dimensional Hypercube Symmetric Quadrature Formulas W5 (6) * and W6 (6) *. They have fewer number of function evaluations relative to the Gaussian Quadrature Equal Accuracy formula, with a minimum of 185 and 505 evaluations, and 465 and 1825 evaluations. The derived four-dimensional and six-dimensional quadrature formulas are respectively applied to the calculation of the impedance element of the RWG-GGM method and the expansion of the non-uniform media target. The calculation results show that in the element of the splitting unit The relative accuracy of the two sets of four-dimensional space quadrature formulas is in the order of 1e-6 under the conventional application where the electrical dimension does not exceed λ / 4. The quadrature accuracy of the two-dimensional space quadrature formula is in the order of 1e-4, and the quadrature effect is ideal .